A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm respectively. Find the height of the bucket.

Explanation

Given volume of the frustum = 28.49 L `= 28.49 xx 1000 cm^(3)" "[therefore 1 L = 1000 cm^(3)] `
`= 28490 cm^(3)`
and radius of the top `(r_(1) )= 28 cm`
radius of the bottom `(r_(2)) = 21 cm`
Let height of the bucket = h cm
Now, volume of the bucket `= (1)/(3) pi h(r_(1)^(2) + r_(2)^(2) + r_(1)r_(2))= 28490 `
`rArr " " (1)/(3) xx (22)/(7) xx h (28^(2) + 21^(2) + 28xx 21) =28490`
`rArr " "h (784 + 441 +588) = (28490xx3xx7)/(22)`
`rArr " " 1813 h = 1925 xx 12`
`therefore" "h=(1295 xx 21)/(1813) = (27915)/(1813) = 15 cm`